First, what is speed? In badminton, The term "speed"
refers to how far a shuttlecock will travel when struck with a standard
force, "further" being considered "faster".
Due to differences of air resistance related to altitude, humidity
and temperature, the same shuttlecock will have a different "speed"
at different locations. A shuttlecock which is good in Hong Kong
may not be good to use in London. Because there's differences in
temperature; humidity; altitude and air pressure etc.

Because of weight differences and other factors, the shuttles come
in varying speeds. The referees are responsible for testing the
shuttles each day and determining what speed will be used that day.
During a round of competition, we can be asked to change the shuttle
speed because conditions - heat and humidity, for instance- have
changed. That can be one of the more difficult disputes since a
slower shuttle might benefit one player¡¯s style while
a faster shuttle would be advantageous for the other.

In an IBF tournament, most of the Chief Referee will test up to
3 different speed of shuttlecocks to ensure that particular speed
is right for that particular place at that particular time.

Fast or slow do not represent the quality of the shuttlecock. But,
of course, the consumer has the right to choose.

From the list, you can see that the shuttles were traditionally
divided into 48, 49, 50, 51, 52 according to the weight of the shuttles.
49 weights 4.9g, 50 means 5.0g, 51 means 5.1g and so on. We found
the shuttles using these rating was inaccurate and therefore was
difficult to classify. So we change the shuttles' speed standard.
We use Speed 75, 76, 77, 78, 79, 80 instead. There is a 30cm distance
between eachspeed. Shuttle speeds are ideal for different parts
of the world. For example, shuttles with Speed 76 are used in China
during the summer and 77 during the winter months. Shuttles with
Speed 75 are good in Thailand, Speed 76 ,77 in Singapore, Hong Kong
and Malaysia, Speed 77, 78 in the U.S.A., Speed 78,79 in Finland,
Canada, Korea and Japan. Speed 79, 80 in Australia in winter. Speed
73-74 would only be played in high altitude area as Yunnan Province
in China and Colorado Springs in U.S.A. or high temperture area
as Johannesburg in South Africa.

Shuttlecocks also have rotational speed which is crucial for the
stabilities. For shuttlecock stability at speeds higher than Mach
0.65, the upper body flaps were moved from the average position
of 11.8 degrees to 20 degrees upward from the body surface.

If you ask what's the maximum speed in kilometers per hour for
the shuttlecock ever got regardless circumstance, please check the
Guinness Book of Records. The shuttlecock is poised to enter the
Guinness Book of Records at 162 miles per hour (261 kph) -- the
speed it travels on the smash -- compared to squash`s 151 mph (243
kph) and a mere 138 mph (222 kph) for tennis. Badminton`s promoters
hope the speed record might bolster the sport`s image and help move
it out of other racket sports` shadows, particularly in regions
where tennis and squash reign supreme. Beside Guinness, I saw somebooks
claiming the speed for shuttlecock is about 300 km/h.

As the shuttlecock flys, two forces affect its motion: gravity
pulling down and air resistance pushing it up. The acceleration
due to gravity is constant. The acceleration due to air resistance
increases as the shuttlecock picks up speed through the air. The
shuttlecock's acceleration, a, along a vertical coordinate axis
with positive down, is given by an equation of the following form:

a = g - f(v)

while f(v) depends on temperature, humidity; altitude and air pressure
etc. Write it in a general form:
a = g - bv^r
here r is within 1 and 2 depends on temperature, humidity; altitude
and air pressure etc.